There are many ways to model binary trees using sets and functions. For this example we will use a definition that relies on some Z notation for describing recursive data structures. The details of the syntax are not terribly important at this point, but you should understand the basic idea about building up trees from other trees.
Here is the definition:
It says that a tree is either a leaf or is made up of two subtrees glued together with node. Usually we would associate some data with the leaf and/or nodes, but for present purposes this simple definition will suffice.
Here are some examples of the kind of structures that we can build up using this definition:
